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This resource index gives users access to most of the course resources in a single location.

Unit I: Ax = b and the Four Subspaces

TITLES LECTURE VIDEOS LECTURE NOTES TEXTBOOK READINGS PROBLEM SOLVING VIDEOS PROBLEM SETS
The Geometry of Linear Equations
Lecture summary (PDF) Sections 1.1, 1.2, and 2.1 in the 4th or 5th edition







Problems (PDF)

Solutions (PDF)

An Overview of Key Ideas
Lecture summary (PDF)

Sections 1.3 in the 4th or 5th edition

None
Elimination with Matrices
Lecture summary (PDF) Section 2.2 through 2.3 in the 4th or 5th edition


Problems (PDF)

Solutions (PDF)

Multiplication and Inverse Matrices
Lecture summary (PDF) Section 2.4 through 2.5 in the 4th or 5th edition


Problems (PDF)

Solutions (PDF)

Factorization into A = LU
Lecture summary (PDF) Section 2.6 in the 4th or 5th edition


Problems (PDF)

Solutions (PDF)

Transposes, Permutations, Vector Spaces
Lecture summary (PDF) Section 2.7 in the 4th or 5th edition







Problems (PDF)

Solutions (PDF)

Column Space and Nullspace
Lecture summary (PDF) Section 3.1 through 3.2 in the 4th or 5th edition


Problems (PDF)

Solutions (PDF)

Solving Ax = 0: Pivot Variables, Special Solutions
Lecture summary (PDF) Section 3.2 in the 4th or 5th edition


Problems (PDF)

Solutions (PDF)

Solving Ax = b: Row Reduced Form R
Lecture summary (PDF) Section 3.3 through 3.4 in the 4th or 5th edition


Problems (PDF)

Solutions (PDF)

Independence, Basis and Dimension
Lecture summary (PDF) Section 3.5 in the 4th edition or Section 3.4 in the 5th edition


Problems (PDF)

Solutions (PDF)

The Four Fundamental Subspaces
Lecture summary (PDF) Section 3.6 in the 4th edition or Section 3.5 in the 5th edition


Problems (PDF)

Solutions (PDF)

Matrix Spaces; Rank 1; Small World Graphs
Lecture summary (PDF) Section 3.3 and 8.2 in the 4th edition or Section 3.3 and 10.1 in the 5th edition


Problems (PDF)

Solutions (PDF)

Graphs, Networks, Incidence Matrices
Lecture summary (PDF) Section 8.2 in the 4th edition or Section 10.1 in the 5th edition


Problems (PDF)

Solutions (PDF)

Exam 1 Review
Lecture summary (PDF) Review Chapters 1, 2, and 3, plus Section 8.2 in the 4th edition or Chapters 1, 2, and 3, plus Section 10.1 in the 5th edition
None

Exam 1

EXAM EXAMS AND SOLUTIONS
Exam 1

Exams (PDF)

Solutions (PDF)

Unit II: Least Squares, Determinants and Eigenvalues

TITLES LECTURE VIDEOS LECTURE NOTES TEXTBOOK READINGS PROBLEM SOLVING VIDEOS PROBLEM SETS
Orthogonal Vectors and Subspaces
Lecture summary (PDF) Section 4.1 in the 4th or 5th edition


Problems (PDF)

Solutions (PDF)

Projections onto Subspaces
Lecture summary (PDF)

Section 4.2 in the 4th or 5th edition



Problems (PDF)

Solutions (PDF)

Projection Matrices and Least Squares
Lecture summary (PDF) Section 4.3 in the 4th or 5th edition


Problems (PDF)

Solutions (PDF)

Orthogonal Matrices and Gram-Schmidt
Lecture summary (PDF) Section 4.4 in the 4th or 5th edition


Problems (PDF)

Solutions (PDF)

Properties of Determinants
Lecture summary (PDF) Section 5.1 in the 4th or 5th edition


Problems (PDF)

Solutions (PDF)

Determinant Formulas and Cofactors
Lecture summary (PDF) Section 5.2 in the 4th or 5th edition







Problems (PDF)

Solutions (PDF)

Cramer’s Rule, Inverse Matrix and Volume
Lecture summary (PDF) Section 5.3 in the 4th or 5th edition







Problems (PDF)

Solutions (PDF)

Eigenvalues and Eigenvectors
Lecture summary (PDF) Section 6.1 through 6.2 in the 4th or 5th edition


Problems (PDF)

Solutions (PDF)

Diagonalization and Powers of A
Lecture summary (PDF) Section 6.2 in the 4th or 5th edition


Problems (PDF)

Solutions (PDF)

Differential Equations and exp(At)
Lecture summary (PDF) Section 6.3 in the 4th or 5th edition







Problems (PDF)

Solutions (PDF)

Markov Matrices; Fourier Series
Lecture summary (PDF) Section 8.3 and 8.5 in the 4th edition or Sections 10.3 and 10.5 in the 5th edition


Problems (PDF)

Solutions (PDF)

Exam 2 Review

 
Lecture summary (PDF) Review Chapters 4, 5, and 6 (through Sec. 6.3) plus Sections 8.3 and 8.5 in the 4th edition or Review Chapters 4, 5, and 6 (through Sec. 6.3) plus Sections 10.3 and 10.5 in the 5th edition





None

Exam 2

EXAM EXAMS AND SOLUTIONS
Exam 2

Exams (PDF)

Solutions (PDF)

Unit III: Positive Definite Matrices and Applications

TITLES LECTURE VIDEOS LECTURE NOTES TEXTBOOK READINGS PROBLEM SOLVING VIDEOS PROBLEM SETS
Symmetric Matrices and Positive Definiteness
Lecture summary (PDF) Section 6.4 through 6.5 in the 4th or 5th edition


Problems (PDF)

Solutions (PDF)

Complex Matrices; Fast Fourier Transform (FFT)
Lecture summary (PDF)

Section 10.2 through 10.3 in the 4th edition or Section 9.2 and 9.3 in the 5th edition



Problems (PDF)

Solutions (PDF)

Positive Definite Matrices and Minima
Lecture summary (PDF) Section 6.5 in the 4th or 5th edition


Problems (PDF)

Solutions (PDF)

Similar Matrices and Jordan Form
Lecture summary (PDF) Section 6.6 in the 4th edition or Section 6.2 in the 5th edition


Problems (PDF)

Solutions (PDF)

Singular Value Decomposition
Lecture summary (PDF) Section 6.7 in the 4th edition or Section 7.1 and 7.2 in the 5th edition


Problems (PDF)

Solutions (PDF)

Linear Transformations and their Matrices
Lecture summary (PDF) Section 7.1 in the 4th edition or Section 8.1 in the 5th edition


Problems (PDF)

Solutions (PDF)

Change of Basis; Image Compression
Lecture summary (PDF) Section 7.2 in the 4th edition or Section 8.2 in the 5th edition


Problems (PDF)

Solutions (PDF)

Left and Right Inverses; Pseudoinverse
Lecture summary (PDF) Section 7.3 in the 4th edition or Section 8.3 in the 5th edition


Problems (PDF)

Solutions (PDF)

Exam 3 Review
Lecture summary (PDF) Review Chapters 6 and 7, plus Sections 10.2 through 10.3 in the 4th edition or Review Chapters 6, 7, and 8 plus Sections 9.2 through 9.3 in the 5th edition
None

Exam 3

EXAM EXAMS AND SOLUTIONS
Exam 3

Exams (PDF)

Solutions (PDF)

Final Course Review

TITLES LECTURE VIDEOS LECTURE NOTES TEXTBOOK READINGS PROBLEM SOLVING VIDEOS PROBLEM SETS
Final Course Review  
Lecture summary (PDF) None  
None

Final Exam

FINAL EXAM EXAMS AND SOLUTIONS
Final Exam

Exams (PDF)

Solutions (PDF)

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